Dynamical Scenarios for Chromosome Bi-orientation Tongli Zhang, Raquel A. Oliveira, Bernhard Schmierer, Béla Novák  Biophysical Journal  Volume 104, Issue 12, Pages 2595-2606 (June 2013) DOI: 10.1016/j.bpj.2013.05.005 Copyright © 2013 Biophysical Society Terms and Conditions

Figure 1 A minimal network representation of the tension hypothesis and its dynamical properties. (A) Network diagram. On both kinetochores, Eraser represses Att. After the formation of bi-orientation, Att and S-Att together generate Tension to repress Eraser and S-Eraser. (B) The mutual antagonism between Att and Eraser. The interaction between Att and Eraser is investigated on a phase plane. The balance curves for Att (blue line) and Eraser (red lines) are plotted in the absence and the presence of S-Att. Att decreases when Eraser activity increases. In the absence of S-Att, Eraser has constant activity (red line) and the steady state is characterized by high Eraser activity and low Att (loose attachment, open circle). In the presence of high S-Att, Eraser is repressed by increasing Att (red dashed line) and the steady state corresponds to strong binding (solid circle). (C) The response of Att to different levels of S-Att. Att and S-Att are either both low or both high. These two states are separated by a threshold. (D) Phase-plane analysis of the mutual activation between Att and S-Att. The balance curve of Att (solid blue line) and of S-Att (dashed blue line) are plotted. Two steady states are surrounded by two attraction basins that are separated by a separatrix (black line), which originates from a saddle point (open square). (Lower-left steady state) Loose attachment (open circle); (upper right) strong attachment (solid circle). Biophysical Journal 2013 104, 2595-2606DOI: (10.1016/j.bpj.2013.05.005) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 2 Two ways of overcoming the initiation problem of the bistable switch model. (A) Stochastic effects can initiate bi-orientation. Representative stochastic time-series simulation. All five variables of the model are shown. (B) Phase-plane plotting of the stochastic trajectory. (Red line and circles) Replotting of the time-dependent changes of Att and S-Att sampled from the representative simulation shown in panel A on the phase plane shown in Fig. 1 D. Note that the trajectory crosses back and forth over the separatrix, indicating that the system can move between the two attraction basins. (C and D) Bi-orientation can be the only steady state if significant attachment can form already in the absence of tension. (C) Signal-response curve. Note the reduced dynamic range when compared to Fig. 1 C. (D) Phase plane. The diagram corresponds to Fig. 1 D, but with R0att=0.8 instead of R0att=0.55. One steady state has disappeared and the system is mono-stable. The bi-oriented configuration has become a global attractor. Biophysical Journal 2013 104, 2595-2606DOI: (10.1016/j.bpj.2013.05.005) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 3 Isolated chromatids show oscillatory movements. Reanalysis of experimental data (34) in pseudo-anaphase (see main text for details). (A) Distances from an initial reference point are plotted for four distinct isolated chromatids. (B) The velocities of the chromatids shown in panel A. Biophysical Journal 2013 104, 2595-2606DOI: (10.1016/j.bpj.2013.05.005) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 4 A trial-and-error oscillator. (A) Modified network diagram. Compared with the initial network in Fig. 1 A, Eraser activity is now promoted by Att, and Eraser promotes its own activity (red arrows). These modifications create a negative feedback loop and a time delay, which are required features of an oscillator. (B) Phase-plane analysis of the oscillator model. Phase plane as in Fig. 1 B, but for the oscillator model. In the absence of S-Att, the intersection between the Att balance curve (blue line) and the Eraser balance curve (red line) results in an unstable steady state (open circle) and a limit cycle oscillation (black line). (Inset) The different phases of the oscillation. If S-Att is high, the intersection between the Att balance curve and the Eraser balance curve (red dashed line) results in a stable steady state with high Att (solid circle). (C) Signal response curve. If S-Att is below a critical threshold, the steady states are unstable (dashed part of the blue curve) and Att oscillates between the indicated minima and maxima (red dots). At suprathreshold levels of S-Att, the oscillation stops and a branch with stable steady states characterized by high Att appears (solid part of the blue curve). (D and E) Time-course plotting of representative stochastic simulations. (D) If the communication between sister kinetochores is disrupted (no tension is created), Att and Eraser, as well as S-Att and S-Eraser, show oscillations. (E) If sisters communicate with each other, Tension is quickly generated and it is maintained throughout (compare to Fig. 2 A). A bi-oriented state is thus efficiently initiated and robustly maintained. (F) Pseudo-phase plane plotting. The signal response curve (C) is plotted as the Att balance curve, while the S-Att balance curve is a mirror picture. The maximal and minimal values of the Att oscillation (circles) and S-Att (squares) are indicated. (Black solid circle) The only stable steady state corresponding to bi-orientation. (Red circles and lines) Replotting of the time-dependent changes of Att and S-Att sampled from the representative simulation shown in panel E. Biophysical Journal 2013 104, 2595-2606DOI: (10.1016/j.bpj.2013.05.005) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 5 A stochastic bistable switch. (A) Network diagram. The positive feedback is implemented with Eraser self-activation. Compared to the oscillator model, the assumption of a negative feedback between Eraser and Att is dropped. (B) Analysis of the model. In the absence of Tension, the intersection between the eraser steady state (Fera, solid red) and Eraser (black) results in two stable steady states (solid circles) separated by an unstable steady state (open circle). If Tension is high, the intersection between Eraser steady state (Fera, dashed red) and Eraser results in one stable steady state with inactive Eraser (solid circle). (C) Signal response curve. If S-Att is below a critical threshold, stable steady states (solid parts of the curve) with either low or high Att are separated by unstable steady states (dashed part of the curve). At suprathreshold levels of S-Att, the stable steady state with low Att disappears. (D and E) Time-course plotting of representative stochastic simulations. (D) In the absence of tension, i.e., if the communication between sister kinetochores is disrupted, Eraser activity switches on and off in a stochastic manner. (E) If sisters communicate with each other, tension is generated and maintained. A desired bi-oriented state is thus initiated and maintained. Note that low Eraser activity allows a time window during which Att can increase independently of S-Att. (F) Pseudo-phase plane plotting. The signal response curve (C) is plotted as the Att balance curve, while the S-Att balance curve is a mirror picture. (Black solid circle) Stable steady states. (Top-right steady state) bi-orientation. (Red circles and line) Time-dependent changes of Att and S-Att sampled from the representative simulation shown in panel E. Biophysical Journal 2013 104, 2595-2606DOI: (10.1016/j.bpj.2013.05.005) Copyright © 2013 Biophysical Society Terms and Conditions